These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Award Snub: Alfred Hitchcock is the most egregious example (although for Psycho, he was nominated for Best Director, but did not win), but many are utterly shocked that Anthony Perkins was never nominated for his performance as Norman Bates. In 2009, Entertainment Weekly considered that snub to be the second worst Oscar snub of all time. Hitchcock himself expressed to Perkins how ashamed he was because Perkins was not nominated. Also, Bernard Hermann's score wasn't nominated either.
The famous repeated minor-9th violin chords during the shower scene were so monstrously effective, they were used again by later generations of horror movie directors in their own films. They even have their own trope page.
It's noted on the Trivia page that Hitchcock originally considered doing the scene without the music. If there was ANY way to make that scene scarier, THAT would have been it, since it would have made it come even more out of nowhere than it already did. In fact, this could be applied to a LOT of horror films to come along since Psycho.
Big Lipped Alligator Moment: The 1998 remake has random, near-subliminal video clips (storm clouds, a sheep in a road, a woman in bondage gear) which pop up during the two murder scenes.
Freud Was Right: Norman's Mommy Issues and sexual repression are probably what drove him insane. Then there's the shower scene, where the knife stabbing is often interpreted as a phallic symbol.
Another example, a personal one for Norman: at one point he's clearly stuttering and hesitating to say "fallacious", because it sounds like "phallus". He eventually settles on saying "falsity".
Genius Bonus: All the paintings in the parlor, but most specifically the painting that Norman takes off the wall in order to spy on Marion, are versions of Susannah and the Elders, a biblical story about two lecherous voyeurs who try to take advantage of an unsuspecting young woman while she's bathing. Also, in part with the bird motifs, Norman accidentally knocks off one of the pictures of birds in Marion's room, which confirms him as the murderer because he "offed the bird" - which, in British slang, is killing a young woman.
Hilarious in Hindsight: Psycho was released 6 years after Hitchcock's Rear Window, where the character of Stella questions where Thorwald, the suspected murderer, would've killed his wife in their apartment. "Of course, the bathtub! It's the only place he could've washed the blood!"
It Was His Sled: At this late date, it's hard to find anybody who isn't familiar with the original movie's plot twists, whether they've actually seen it or not.
Jerkass Woobie: Lila in the second movie. She's motivated by Norman murdering her sister, so you can understand her personal grief. However, she is downright vindictive towards a person that paid his debt to society and trying to move on with his life, so she is not that sympathetic.
Narm: "Mother, oh God, mother...blood! Blood!" Mostly because they are the only piece of dialogue in a lengthy segment with no dialogue at all and thus seem out of place.
Averted in at least the Italian dubbing, where he frantically asks "Mother, for the love of God, mother! Where does all this blood come from?"
The ending scene in the fruit cellar. While Lila's screaming would have brought anyone down to the fruit cellar, the fact that when Norman realized she was in the house that he went up to his mother's room to dress up as her instead of having a quick look around and then going down to the fruit cellar kind of detracts from the seriousness. Not much, but some.
The Scrappy: The psychiatrist is considered one for his long-winded scene that comes at the end of the film, which states information that should be largely obvious by the end.
Sequelitis: Averted with the surprisingly-good Psycho II. YMMV on the other sequels, but the common consensus seems to be that Psycho III is visually interesting but flawed and lacking in depth, whereas Psycho IV is just plain lousy, albeit not completely awful. The remake and the 1987 film Bates Moteldo not count.
This also occurred with a different sequel to the original novel, and another plot was bandied about elsewhere: with Norman being released, found to be cured, back into the general populace. Except it was the 70s, when he went away in the early 60s. The eponymous "psycho" would have been the Anvilicious world around him.
The Woobie: Norman. He's so epically messed up. His father dies when he is 5 (it's never made clear how this happened). After this, his mother deliberately isolates and dominates him, making him dependent on her. She also fills his head with how sinful and evil women are. Then she shows up with a man when Norman is age 12. At this point, there are two possibilities: Norman is angry and jealous and kills both mother and her lover. Or, Mrs Bates kills both herself and her lover (remember the deceased Mr Bates). For option A, Norman is wracked with guilt and retrieves his mother's corpse as well as internalising her in order to alleviate his remorse. For option B, Norman simply assumes guilt for his mother's death (easier than confronting her abandonment of him) - and then internalises her. Either way, the woman who was responsible for his abusive childhood now lives inside his head, berating, watching, punishing - no peace, nowhere to hide. Norman's trap is his own mind, and he can't escape. Hitchcock deliberately cast Anthony Perkins in the role to emphasise Norman's woobie quality. The sequels trade heavily on it, too - especially Psycho II.
You may feel even worse for him in the second movie, as you know all of this going in. We see that he served his time and met the requirements to be released. He so desperately tries to get his life in order and maintain his newfound sanity, but he's being pushed over the edge due to a personal vendetta.
What The Hell, Casting Agency?: Vince Vaughn as Norman Bates in the remake. Also, taking the Janet Leigh part of the sexy, tempting woman who awakens "Mother" - bony, spiky-haired Anne Heche. Roger Ebert went so far to say that William H. Macy was the only actor who was appropriately cast.